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New from this chapter
\(P \cdot V_{\mathrm{gas}} = n \cdot R \cdot T\)
chemical amount of a pure gas (ideal gas law)
\(P_{\mathrm{component}} \cdot V_{\mathrm{gas}} = n_{\mathrm{component}} \cdot R \cdot T\)
chemical amount of a gas component
\(P_{\mathrm{total}} = \sum (P_{\mathrm{partial}})\)
Additivity of partial pressure
\(X_{\mathrm{A}} = \dfrac{n_{\mathrm{A}}}{n_{\mathrm{total}}}\)
definition of mole fraction
\(E_{\mathrm{kin\ avg}} = \dfrac{3}{2} \cdot R \cdot T\)
average molar kinetic energy of particle at given temperature
\(P_{\mathrm{A}} = X_{\mathrm{a}} \cdot P_{\mathrm{total}}\)
partial pressure from mole fraction
\(P = \dfrac{F}{A}\)
Definition of pressure
\(P_{\mathrm{hydrostatic}} = h \cdot ρ_{\mathrm{fluid}} \cdot g_{\mathrm{0}}\)
Hydrostatic pressure
\(\mathrm{rate}_{\mathrm{diffusion}} = \dfrac{n_{\mathrm{gas\ area}}}{Δt}\)
definition of rate of diffusion
\(\dfrac{\mathrm{rate}_{\mathrm{effusion\ A}}}{\mathrm{rate}_{\mathrm{effusion\ B}}} = \sqrt{\dfrac{m_{\mathrm{B}}}{m_{\mathrm{A}}}} = \sqrt{\dfrac{M_{\mathrm{B}}}{M_{\mathrm{A}}}}\)
molar mass dependence of rate of effusion
\(u_{\mathrm{rms}} = \sqrt{\dfrac{{u_{\mathrm{1}}}^{2} + {u_{\mathrm{2}}}^{2} + {u_{\mathrm{3}}}^{2} + {u_{\mathrm{4}}}^{2} \cdot ...}{n}}\)
definition of rms particle speed
\(u_{\mathrm{rms}} = \sqrt{\dfrac{2 \cdot E_{\mathrm{kin\ avg}} \cdot N_{\mathrm{A}}}{m_{\mathrm{particle}}}} = \sqrt{\dfrac{3 \cdot R \cdot T}{M_{\mathrm{particle}}}}\)
velocity of gas particle
\(Z = \dfrac{V_{\mathrm{molar\ measured}}}{V_{\mathrm{molar\ ideal}}} = \dfrac{P \cdot V_{\mathrm{molar\ measured}}}{R \cdot T}\)
non-ideality of gas
\((P + \dfrac{{n}^{2} \cdot a}{{V_{\mathrm{gas}}}^{2}}) \cdot (V_{\mathrm{gas}} - n \cdot b) = n \cdot R \cdot T\)
non-ideal gas law
From previous chapters
...important for many chemistry topics (you should know these by heart)
chemical amount from mass of a pure substance
chemical amount of a solute
chemical amounts in a chemical reaction (stoichiometry)
finding the limiting reactant
...might need one of those
\(ρ_{\mathrm{sample}} = \dfrac{m_{\mathrm{sample}}}{V_{\mathrm{sample}}}\)
Definition of density
\(N_{\mathrm{charge}} = N_{\mathrm{\ce{p+}}} - N_{\mathrm{\ce{e-}}}\)
protons and electrons have opposite charges
\(c_{\mathrm{1}} \cdot V_{\mathrm{1}} = c_{\mathrm{2}} \cdot V_{\mathrm{2}}\)
Dilution law
\(n_{\mathrm{1}} = ν \cdot n_{\mathrm{2}}\)
stoichiometric ratio (shortcut)
\(n_{\mathrm{1}} = ν_{\mathrm{1}} \cdot n_{\mathrm{\ce{->}}}\)
using chemical amount of reaction
\(\mathrm{Charge}_{\mathrm{species}} = \sum (N_{\mathrm{atom}} \cdot \mathrm{Ox}_{\mathrm{atom}})\)
Sum of oxidation number
\(n_{\mathrm{theoretical\ yield}} = n_{\mathrm{\ce{->}}} \cdot ν_{\mathrm{\ce{product}}}\)
calculating theoretical yield (based on chemical amount)
\(m_{\mathrm{theoretical\ yield}} = n_{\mathrm{\ce{->}}} \cdot ν_{\mathrm{\ce{product}}} \cdot M_{\mathrm{\ce{product}}}\)
calculating theoretical yield (by mass)
\(\mathrm{yield}_{\mathrm{rel}} = \dfrac{n_{\mathrm{actual}}}{n_{\mathrm{theoretical}}} \cdot 100\ \mathrm{％}\)
Calculating percent yield from amounts
\(\mathrm{yield}_{\mathrm{rel}} = \dfrac{m_{\mathrm{actual}}}{m_{\mathrm{theoretical}}} \cdot 100\ \mathrm{％}\)
Calculating percent yield from masses
...less likely
\(N_{\mathrm{A}} = \dfrac{N_{\mathrm{particle}}}{n_{\mathrm{particle}}}\)
definition Avogadro's constant
\(\mathrm{fraction}_{\mathrm{bymass}} = \dfrac{m_{\mathrm{solute}}}{m_{\mathrm{solution}}} \cdot 100\ \mathrm{％}\)
definition concentration as mass fraction in percent
\(\mathrm{fraction}_{\mathrm{byvolume}} = \dfrac{V_{\mathrm{solute}}}{V_{\mathrm{solution}}}\)
definition concentration as volume fraction in percent
\(\mathrm{ppm} = \dfrac{1}{1000000}\)
definition ppm
\(\mathrm{ppb} = 1\times 10^{-9}\)
definition ppb
\(N_{\mathrm{atoms}} = \mathrm{coeff} \cdot \mathrm{subscript}\)
Counting atoms in formula or chemical equation
\(ΔU = q + w\)
First law of thermodynamics
\(ΔH_{\mathrm{reaction}} = \sum (n_{\mathrm{prod}} \cdot ΔH_{\mathrm{f,prod}}) - \sum (n_{\mathrm{react}} \cdot ΔH_{\mathrm{f,react}})\)
Enthalpy from heats of formation
\(E_{\mathrm{photon}} = h_{\mathrm{Planck}} \cdot ν\)
Photon: Energy vs frequency
\(\mathrm{charge}_{\mathrm{formal}} = ⋕e_{\mathrm{outer\ freeatom}} - ⋕e_{\mathrm{lonepairs}} - \dfrac{1}{2} \cdot ⋕e_{\mathrm{bonding}}\)
Definition of formal charge
\(D_{\mathrm{\ce{X-Y}}} = ΔH_{\mathrm{bonddissociation}}\)
Definition of bond energy
\(\mathrm{order}_{\mathrm{bond}} = \dfrac{⋕e_{\mathrm{bonding}} - ⋕e_{\mathrm{antibonding}}}{2}\)
definition bond order